sat suite question viewer

Algebra / Linear inequalities in one or two variables Difficulty: Medium

The length of a rectangle is $50$ inches and the width is $x$ inches. The perimeter is at most $210$ inches. Which inequality represents this situation?

Back question 57 of 73 Next

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73

Explanation

Choice A is correct. The perimeter of a rectangle is equal to the sum of $2$ times its length and $2$ times its width. It's given that the rectangle's length is $50$ inches and the width is $x$ inches. Therefore, the perimeter, in inches, is $2 left parenthesis 50 right parenthesis plus 2 x$ , or $100 plus 2 x$ , which is equivalent to $2 x plus 100$ . It's given that the perimeter is at most $210$ inches; therefore, $2 x + 100 \leq 210$ represents this situation.

Choice B is incorrect. This inequality represents a situation where the perimeter is at least, rather than at most, $210$ inches.

Choice C is incorrect. This inequality represents a situation where $2$ times the length, rather than the length, is $50$ inches.

Choice D is incorrect. This inequality represents a situation where $2$ times the length, rather than the length, is $50$ inches, and the perimeter is at least, rather than at most, $210$ inches.